Theorems · Theorem · commutative algebra

Module.free_of_finite_type_torsion_free

∀ {ι : Type u_1} {R : Type u_2} [inst : CommRing R] {M : Type u_3} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [IsPrincipalIdealRing R] [IsDomain R] [Finite ι] {s : ι → M},
  Submodule.span R (Set.range s) = ⊤ → ∀ [Module.IsTorsionFree R M], Module.Free R M

Defined in: Mathlib.LinearAlgebra.FreeModule.PID
Cited by: 0 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsPrincipalIdealRing IsDomain Finite Module.IsTorsionFree

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Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Top.topstatement and proof · cited by 9,680
Fintypeproof · cited by 7,736
Submodulestatement · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Finitestatement and proof · cited by 3,029
IsDomainstatement and proof · cited by 2,196
Submodule.spanstatement and proof · cited by 1,504
Module.Basisproof · cited by 1,477
Module.IsTorsionFreestatement and proof · cited by 600

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